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Iterative Born solver for the acoustic Helmholtz equation with heterogeneous sound speed and density.

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Title: Iterative Born solver for the acoustic Helmholtz equation with heterogeneous sound speed and density.
Authors: Stanziola, Antonio1 (AUTHOR) stanziola.antonio@gmail.com, Arridge, Simon R.2 (AUTHOR), Treeby, Bradley E.1 (AUTHOR), Cox, Benjamin T.1 (AUTHOR) b.cox@ucl.ac.uk
Source: Journal of the Acoustical Society of America. Feb2026, Vol. 159 Issue 2, p1457-1470. 14p.
Subjects: Helmholtz equation, Born approximation, Iterative methods (Mathematics), Density, Ultrasonic imaging, Inhomogeneous materials, Speed of sound, Fast Fourier transforms
Abstract: Efficient numerical solution of the acoustic Helmholtz equation in heterogeneous media remains challenging, particularly for large-scale problems with spatially varying density—a limitation that restricts applications in biomedical acoustics and seismic imaging. A fast iterative solver that extends the convergent Born series [Osnabrugge, Leedumrongwatthanakun, and Vellekoop, J. Comput. Phys. 322, 113–124 (2016)] method to handle arbitrary variations in sound speed, density, and absorption simultaneously is presented. This approach reformulates the Helmholtz equation as a first-order system and applies the universal split-preconditioner from Vettenburg and Vellekoop [arXiv:2207.14222v2 (2022)], yielding a matrix-free algorithm that leverages Fast Fourier Transforms for computational efficiency. Unlike existing Born series methods, this solver accommodates heterogeneous density without requiring expensive matrix decompositions or preprocessing steps, making it suitable for large-scale three-dimensional problems with minimal memory overhead. The method provides forward and adjoint solutions, enabling its application for inverse problems. Accuracy is validated through comparison against an analytical solution and the solver's practical utility is demonstrated through transcranial ultrasound simulations. The solver achieves convergence for strong scattering scenarios, offering a computationally efficient alternative to time-domain methods and matrix-based Helmholtz solvers for applications ranging from medical ultrasound treatment planning to seismic exploration. [ABSTRACT FROM AUTHOR]
Copyright of Journal of the Acoustical Society of America is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 191986398
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PubTypeId: academicJournal
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  Data: Iterative Born solver for the acoustic Helmholtz equation with heterogeneous sound speed and density.
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  Data: <searchLink fieldCode="AR" term="%22Stanziola%2C+Antonio%22">Stanziola, Antonio</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> stanziola.antonio@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Arridge%2C+Simon+R%2E%22">Arridge, Simon R.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Treeby%2C+Bradley+E%2E%22">Treeby, Bradley E.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Cox%2C+Benjamin+T%2E%22">Cox, Benjamin T.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> b.cox@ucl.ac.uk</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+the+Acoustical+Society+of+America%22">Journal of the Acoustical Society of America</searchLink>. Feb2026, Vol. 159 Issue 2, p1457-1470. 14p.
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  Data: <searchLink fieldCode="DE" term="%22Helmholtz+equation%22">Helmholtz equation</searchLink><br /><searchLink fieldCode="DE" term="%22Born+approximation%22">Born approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Density%22">Density</searchLink><br /><searchLink fieldCode="DE" term="%22Ultrasonic+imaging%22">Ultrasonic imaging</searchLink><br /><searchLink fieldCode="DE" term="%22Inhomogeneous+materials%22">Inhomogeneous materials</searchLink><br /><searchLink fieldCode="DE" term="%22Speed+of+sound%22">Speed of sound</searchLink><br /><searchLink fieldCode="DE" term="%22Fast+Fourier+transforms%22">Fast Fourier transforms</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Efficient numerical solution of the acoustic Helmholtz equation in heterogeneous media remains challenging, particularly for large-scale problems with spatially varying density—a limitation that restricts applications in biomedical acoustics and seismic imaging. A fast iterative solver that extends the convergent Born series [Osnabrugge, Leedumrongwatthanakun, and Vellekoop, J. Comput. Phys. 322, 113–124 (2016)] method to handle arbitrary variations in sound speed, density, and absorption simultaneously is presented. This approach reformulates the Helmholtz equation as a first-order system and applies the universal split-preconditioner from Vettenburg and Vellekoop [arXiv:2207.14222v2 (2022)], yielding a matrix-free algorithm that leverages Fast Fourier Transforms for computational efficiency. Unlike existing Born series methods, this solver accommodates heterogeneous density without requiring expensive matrix decompositions or preprocessing steps, making it suitable for large-scale three-dimensional problems with minimal memory overhead. The method provides forward and adjoint solutions, enabling its application for inverse problems. Accuracy is validated through comparison against an analytical solution and the solver's practical utility is demonstrated through transcranial ultrasound simulations. The solver achieves convergence for strong scattering scenarios, offering a computationally efficient alternative to time-domain methods and matrix-based Helmholtz solvers for applications ranging from medical ultrasound treatment planning to seismic exploration. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of the Acoustical Society of America is the property of American Institute of Physics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1121/10.0042259
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      – Code: eng
        Text: English
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        PageCount: 14
        StartPage: 1457
    Subjects:
      – SubjectFull: Helmholtz equation
        Type: general
      – SubjectFull: Born approximation
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
      – SubjectFull: Density
        Type: general
      – SubjectFull: Ultrasonic imaging
        Type: general
      – SubjectFull: Inhomogeneous materials
        Type: general
      – SubjectFull: Speed of sound
        Type: general
      – SubjectFull: Fast Fourier transforms
        Type: general
    Titles:
      – TitleFull: Iterative Born solver for the acoustic Helmholtz equation with heterogeneous sound speed and density.
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            NameFull: Stanziola, Antonio
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            NameFull: Arridge, Simon R.
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            NameFull: Treeby, Bradley E.
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              M: 02
              Text: Feb2026
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              Y: 2026
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